7.96/3.65	YES
9.55/4.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.55/4.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.55/4.15	
9.55/4.15	
9.55/4.15	H-Termination with start terms of the given HASKELL could be proven:
9.55/4.15	
9.55/4.15	(0) HASKELL
9.55/4.15	(1) LR [EQUIVALENT, 0 ms]
9.55/4.15	(2) HASKELL
9.55/4.15	(3) BR [EQUIVALENT, 0 ms]
9.55/4.15	(4) HASKELL
9.55/4.15	(5) COR [EQUIVALENT, 0 ms]
9.55/4.15	(6) HASKELL
9.55/4.15	(7) Narrow [SOUND, 0 ms]
9.55/4.15	(8) QDP
9.55/4.15	(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.55/4.15	(10) YES
9.55/4.15	
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(0)
9.55/4.15	Obligation:
9.55/4.15	mainModule Main 
9.55/4.15	module Main where {
9.55/4.15	import qualified Prelude;
9.55/4.15	}
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(1) LR (EQUIVALENT)
9.55/4.15	Lambda Reductions:
9.55/4.15	The following Lambda expression
9.55/4.15	"\_->q"
9.55/4.15	is transformed to
9.55/4.15	"gtGt0 q _ = q;
9.55/4.15	"
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(2)
9.55/4.15	Obligation:
9.55/4.15	mainModule Main 
9.55/4.15	module Main where {
9.55/4.15	import qualified Prelude;
9.55/4.15	}
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(3) BR (EQUIVALENT)
9.55/4.15	Replaced joker patterns by fresh variables and removed binding patterns.
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(4)
9.55/4.15	Obligation:
9.55/4.15	mainModule Main 
9.55/4.15	module Main where {
9.55/4.15	import qualified Prelude;
9.55/4.15	}
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(5) COR (EQUIVALENT)
9.55/4.15	Cond Reductions:
9.55/4.15	The following Function with conditions
9.55/4.15	"randomSelect (x : []) = x;
9.55/4.15	randomSelect (x : xs)|terminatorrandomSelect xs|otherwisex;
9.55/4.15	"
9.55/4.15	is transformed to
9.55/4.15	"randomSelect (x : []) = randomSelect3 (x : []);
9.55/4.15	randomSelect (x : xs) = randomSelect2 (x : xs);
9.55/4.15	"
9.55/4.15	"randomSelect0 x xs True = x;
9.55/4.15	"
9.55/4.15	"randomSelect1 x xs True = randomSelect xs;
9.55/4.15	randomSelect1 x xs False = randomSelect0 x xs otherwise;
9.55/4.15	"
9.55/4.15	"randomSelect2 (x : xs) = randomSelect1 x xs terminator;
9.55/4.15	"
9.55/4.15	"randomSelect3 (x : []) = x;
9.55/4.15	randomSelect3 wv = randomSelect2 wv;
9.55/4.15	"
9.55/4.15	The following Function with conditions
9.55/4.15	"undefined |Falseundefined;
9.55/4.15	"
9.55/4.15	is transformed to
9.55/4.15	"undefined  = undefined1;
9.55/4.15	"
9.55/4.15	"undefined0 True = undefined;
9.55/4.15	"
9.55/4.15	"undefined1  = undefined0 False;
9.55/4.15	"
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(6)
9.55/4.15	Obligation:
9.55/4.15	mainModule Main 
9.55/4.15	module Main where {
9.55/4.15	import qualified Prelude;
9.55/4.15	}
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(7) Narrow (SOUND)
9.55/4.15	Haskell To QDPs
9.55/4.15	
9.55/4.15	digraph dp_graph {
9.55/4.15	node [outthreshold=100, inthreshold=100];1[label="putStr",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.55/4.15	3[label="putStr ww3",fontsize=16,color="burlywood",shape="triangle"];50[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];3 -> 50[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	50 -> 4[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	51[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 51[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	51 -> 5[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	4[label="putStr (ww30 : ww31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
9.55/4.15	5[label="putStr []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.55/4.15	6 -> 8[label="",style="dashed", color="red", weight=0];
9.55/4.15	6[label="putChar ww30 >> putStr ww31",fontsize=16,color="magenta"];6 -> 9[label="",style="dashed", color="magenta", weight=3];
9.55/4.15	7[label="output",fontsize=16,color="black",shape="triangle"];7 -> 10[label="",style="solid", color="black", weight=3];
9.55/4.15	9 -> 3[label="",style="dashed", color="red", weight=0];
9.55/4.15	9[label="putStr ww31",fontsize=16,color="magenta"];9 -> 11[label="",style="dashed", color="magenta", weight=3];
9.55/4.15	8[label="putChar ww30 >> ww4",fontsize=16,color="black",shape="triangle"];8 -> 12[label="",style="solid", color="black", weight=3];
9.55/4.15	10[label="randomSelect (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
9.55/4.15	11[label="ww31",fontsize=16,color="green",shape="box"];12[label="putChar ww30 >>= gtGt0 ww4",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
9.55/4.15	13[label="randomSelect2 (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
9.55/4.15	14[label="primbindIO (putChar ww30) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
9.55/4.15	15[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
9.55/4.15	16 -> 18[label="",style="dashed", color="red", weight=0];
9.55/4.15	16[label="primbindIO (seq ww30 output) (gtGt0 ww4)",fontsize=16,color="magenta"];16 -> 19[label="",style="dashed", color="magenta", weight=3];
9.55/4.15	17[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) ter0m",fontsize=16,color="burlywood",shape="box"];52[label="ter0m/False",fontsize=10,color="white",style="solid",shape="box"];17 -> 52[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	52 -> 20[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	53[label="ter0m/True",fontsize=10,color="white",style="solid",shape="box"];17 -> 53[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	53 -> 21[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	19 -> 7[label="",style="dashed", color="red", weight=0];
9.55/4.15	19[label="output",fontsize=16,color="magenta"];18[label="primbindIO (seq ww30 ww5) (gtGt0 ww4)",fontsize=16,color="black",shape="triangle"];18 -> 22[label="",style="solid", color="black", weight=3];
9.55/4.15	20[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
9.55/4.15	21[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
9.55/4.15	22[label="primbindIO (enforceWHNF (WHNF ww30) ww5) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3];
9.55/4.15	23[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3];
9.55/4.15	24[label="randomSelect (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];24 -> 27[label="",style="solid", color="black", weight=3];
9.55/4.15	25[label="primbindIO ww5 (gtGt0 ww4)",fontsize=16,color="burlywood",shape="box"];54[label="ww5/IO ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 54[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	54 -> 28[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	55[label="ww5/AProVE_IO ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 55[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	55 -> 29[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	56[label="ww5/AProVE_Exception ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 56[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	56 -> 30[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	57[label="ww5/AProVE_Error ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 57[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	57 -> 31[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	26[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];26 -> 32[label="",style="solid", color="black", weight=3];
9.55/4.15	27[label="randomSelect2 (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];27 -> 33[label="",style="solid", color="black", weight=3];
9.55/4.15	28[label="primbindIO (IO ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];28 -> 34[label="",style="solid", color="black", weight=3];
9.55/4.15	29[label="primbindIO (AProVE_IO ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];29 -> 35[label="",style="solid", color="black", weight=3];
9.55/4.15	30[label="primbindIO (AProVE_Exception ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];30 -> 36[label="",style="solid", color="black", weight=3];
9.55/4.15	31[label="primbindIO (AProVE_Error ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];31 -> 37[label="",style="solid", color="black", weight=3];
9.55/4.15	32[label="aIOE IOError_FullError",fontsize=16,color="black",shape="box"];32 -> 38[label="",style="solid", color="black", weight=3];
9.55/4.15	33[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];33 -> 39[label="",style="solid", color="black", weight=3];
9.55/4.15	34[label="error []",fontsize=16,color="red",shape="box"];35[label="gtGt0 ww4 ww50",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3];
9.55/4.15	36[label="AProVE_Exception ww50",fontsize=16,color="green",shape="box"];37[label="AProVE_Error ww50",fontsize=16,color="green",shape="box"];38[label="AProVE_Exception (AET_IOError (IOError IOError_FullError [] [] Nothing))",fontsize=16,color="green",shape="box"];39[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) ter1m",fontsize=16,color="burlywood",shape="box"];58[label="ter1m/False",fontsize=10,color="white",style="solid",shape="box"];39 -> 58[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	58 -> 41[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	59[label="ter1m/True",fontsize=10,color="white",style="solid",shape="box"];39 -> 59[label="",style="solid", color="burlywood", weight=9];
9.55/4.15	59 -> 42[label="",style="solid", color="burlywood", weight=3];
9.55/4.15	40[label="ww4",fontsize=16,color="green",shape="box"];41[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];41 -> 43[label="",style="solid", color="black", weight=3];
9.55/4.15	42[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
9.55/4.15	43[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3];
9.55/4.15	44[label="randomSelect (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3];
9.55/4.15	45[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
9.55/4.15	46[label="randomSelect3 (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];46 -> 48[label="",style="solid", color="black", weight=3];
9.55/4.15	47[label="aIOE IOError_PermDenied",fontsize=16,color="black",shape="box"];47 -> 49[label="",style="solid", color="black", weight=3];
9.55/4.15	48[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];49[label="AProVE_Exception (AET_IOError (IOError IOError_PermDenied [] [] Nothing))",fontsize=16,color="green",shape="box"];}
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(8)
9.55/4.15	Obligation:
9.55/4.15	Q DP problem:
9.55/4.15	The TRS P consists of the following rules:
9.55/4.15	
9.55/4.15	   new_putStr(:(ww30, ww31)) -> new_putStr(ww31)
9.55/4.15	
9.55/4.15	R is empty.
9.55/4.15	Q is empty.
9.55/4.15	We have to consider all minimal (P,Q,R)-chains.
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(9) QDPSizeChangeProof (EQUIVALENT)
9.55/4.15	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
9.55/4.15	
9.55/4.15	From the DPs we obtained the following set of size-change graphs:
9.55/4.15	*new_putStr(:(ww30, ww31)) -> new_putStr(ww31)
9.55/4.15	The graph contains the following edges 1 > 1
9.55/4.15	
9.55/4.15	
9.55/4.15	----------------------------------------
9.55/4.15	
9.55/4.15	(10)
9.55/4.15	YES
9.81/4.19	EOF